Lattice structure of pseudorandom sequences from shift-register generators

Shu Tezuka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

The author develops a theory of the lattice structure of pseudorandom sequences from shift register generators, i.e., Tausworthe sequences and GFSR (generalized feedback shift register) sequences. The author defines an analog of linear congruential sequences in GF{2,x}, the field of all Laurent series over the Galois field of two elements GF(2), and shows that this class of sequences contains as a subclass the Tausworthe sequence. He derives a theorem that links the k-distribution of such sequences and the successive minima of the k-dimensional lattice over GF{2,x} associated with the sequences, thereby leading to the geometric interpretation of the lattice structure in the k-dimensional unit space of these sequences. This result is generalized to define the successive minima for the point set of k-dimensional vectors each consisting of k consecutive terms of GFSR sequences, and it is shown that GFSR sequences have a similar structure to that of Tausworthe sequences. A simulation problem in which shift-register-type pseudorandom sequences yield useless results due to such lattice structures is discussed.

Original languageEnglish
Title of host publication90 Winter Simulation Conf.
PublisherPubl by IEEE
Pages266-267
Number of pages2
ISBN (Print)0911801723
Publication statusPublished - Dec 1990
Externally publishedYes
Event1990 Winter Simulation Conference Proceedings - New Orleans, LA, USA
Duration: Dec 9 1990Dec 12 1990

Other

Other1990 Winter Simulation Conference Proceedings
CityNew Orleans, LA, USA
Period12/9/9012/12/90

Fingerprint

Pseudorandom Sequence
Shift registers
Lattice Structure
Generator
Feedback
Laurent Series
Set of points
Galois field
Consecutive

All Science Journal Classification (ASJC) codes

  • Chemical Health and Safety
  • Software
  • Safety, Risk, Reliability and Quality
  • Applied Mathematics
  • Modelling and Simulation

Cite this

Tezuka, S. (1990). Lattice structure of pseudorandom sequences from shift-register generators. In 90 Winter Simulation Conf. (pp. 266-267). Publ by IEEE.

Lattice structure of pseudorandom sequences from shift-register generators. / Tezuka, Shu.

90 Winter Simulation Conf.. Publ by IEEE, 1990. p. 266-267.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Tezuka, S 1990, Lattice structure of pseudorandom sequences from shift-register generators. in 90 Winter Simulation Conf.. Publ by IEEE, pp. 266-267, 1990 Winter Simulation Conference Proceedings, New Orleans, LA, USA, 12/9/90.
Tezuka S. Lattice structure of pseudorandom sequences from shift-register generators. In 90 Winter Simulation Conf.. Publ by IEEE. 1990. p. 266-267
Tezuka, Shu. / Lattice structure of pseudorandom sequences from shift-register generators. 90 Winter Simulation Conf.. Publ by IEEE, 1990. pp. 266-267
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